Nonlinear spectroscopy has revealed long-lasting oscillations in the optical response of a variety of photosynthetic complexes. Different theoretical models that involve the coherent coupling of electronic (excitonic) or electronic-vibrational (vibronic) degrees of freedom have been put forward to explain these observations. The ensuing debate concerning the relevance of either mechanism may have obscured their complementarity. To illustrate this balance, we quantify how the excitonic delocalization in the LH2 unit of Rhodopseudomonas acidophila purple bacterium leads to correlations of excitonic energy fluctuations, relevant coherent vibronic coupling, and importantly, a decrease in the excitonic dephasing rates. Combining these effects, we identify a feasible origin for the long-lasting oscillations observed in fluorescent traces from time-delayed two-pulse single-molecule experiments performed on this photosynthetic complex and use this approach to discuss the role of this complementarity in other photosynthetic systems.